Polynomial gaps below linear growth for Kreiss bounded semigroups and operators

Abstract

We prove that every Kreiss bounded $C_0$-semigroup $(T_t)_{t\geq0}$ on a Hilbert space satisfies \[ \|T_t\|\leq C(1+t)^{1-\varepsilon_K}, \qquad t\geq0, \] where $\varepsilon_K>0$ depends explicitly only on the Kreiss constant. The same conclusion is obtained for positive Kreiss bounded $C_0$-semigroups on $L^p$-spaces, $1<p<\infty$, and in discrete time for Kreiss bounded operators on Hilbert spaces and positive Kreiss bounded operators on $L^p$-spaces. Finally, we obtain a non-quantitative polynomial gap for individually eventually positive Kreiss bounded $C_0$-semigroups on $L^p$-spaces.

Disclosure

“(Z; H) ∩ ℓ2 (Z; H) is dense in ℓ2 (Z; H), this proves (23) and the multiplier identity (24) extends by density. □ Declaration on the use of generative AI. The author used ChatGPT (GPT-5.6 Sol, OpenAI) during the preparation of this manuscript for language editing, presentation, and exploratory feedback. All mathematical content was independently verified by the author, who takes full responsibility for the manuscri”

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Multiplier

1

Verified

2026-08-23T05:13:55.050442Z

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